Properties

Label 58800.d
Number of curves $2$
Conductor $58800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.d1 58800gg2 \([0, -1, 0, -6870208, -7331161088]\) \(-7620530425/526848\) \(-2479325614080000000000\) \([]\) \(3732480\) \(2.8561\)  
58800.d2 58800gg1 \([0, -1, 0, 479792, -10561088]\) \(2595575/1512\) \(-7115411520000000000\) \([]\) \(1244160\) \(2.3068\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 58800.d have rank \(1\).

Complex multiplication

The elliptic curves in class 58800.d do not have complex multiplication.

Modular form 58800.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 6q^{11} - q^{13} + 3q^{17} - 4q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.